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Note on lexicographic‐order preservation and stochastic dominance
Authors:Irving H. Lavalle  Peter C. Fishburn
Abstract:This note concerns two issues left unresolved in our study of lexicographic‐order preservation and stochastic dominance in settings where preferences are represented by utility vectors, ordered lexicographically, and judgements emerge as matrices that premultiply utility vectors in expected utility sums. First, a generalization of the ‘Conjecture Σ’, which implied transitivity of a stochastic dominance relation under non‐vacuous resolution‐level information, is proved. Second, this paper comments on using resolution‐level information in higher as well as in first degree stochastic dominance analysis. Copyright © 1999 John Wiley & Sons, Ltd.
Keywords:lexicographic utility  stochastic dominance  matrix probabilities  lexicographic‐order preservation  non‐Archimedean decision theory
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